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1
GPS
GPS (Global Positioning System)
(Space Geodesy) GPS
(local)(regional)
(global) GPS
GPS
GPS
GPS
[1996] GPS
GPS
GPS
GPS 105 617
[,1997]
()
GPS
2
Wells et al (1986), Seeber
(1993) ,Leick (1995) Hofmann-Wellenhof et al (1997)
1
GPS NAVSTAR GPS (NAVigation Satellite with Time and Ranging Global
Positioning System)
GPS
1973
(range) GPS (signal)
(resection method)
(clock) GPS
GPS
GPS
(space segment)(control segment)(user segment)
GPS 24 20,200
55 1995
4 27 GPS
15
GPS L ( L1
L2) 10.23 MHz L 154 120
L1 L2 (L)()
L1= 1575.42 MHz = 19 cm
L2= 1227.60 MHz = 24 cm
PRN (pseudo random noise code)
C/A (coarse acquisition) 300 m
L11.023 MHzC/A(unencrypted)
P (precise)
30 m 10.23 MHz ,
L1 L2 P
(encrypted) Y
GPS 1
10.23 MHz
L11575.42 MHz
L21227.60 MHz
C/A 1.023 MHz
P 10.23 MHz
P 10.23 MHz
x1x0.1
x154
x120
50 BPS
1 GPS
GPS Colorado Springs Falcon
Colorado Springs, Hawaii, Ascension
Island, Diego Garcia Kwajalein
GPS
GPS
3
4
[Shank et al, 1994] L
Kalman
(satellite-state estimates)
S
(broadcast ephemeris)
GPS GPS
()
GPS GPS
2 GPS
GPS
(pseudo-range)
(carrier phase)
(bias)
1% 0.1 ms P
30 cm 10 P C/A
3 m [Wells et al, 1986]
GPS
C/A P
19 cm L1
2 mm
3
Doppler
s(t) s t r() r
rs()
5
rs s
rt( ) ( ) ( )= (1)
GPS
N (integer ambiguity)
(loss of lock)
[CCC1]: Page: 8 3-1
[CCC2]: Page: 8
(cycle slip)
GPS
GPS GPS
(PR) t
(c),
PR c trs
rs= ( ) (2)
GPS T dt
d
6
r r
s s
rs
rs
rs
rs
c d t dt
c t c d dt
= + +
= +
[( ) ( )]
( ) ( )
c T T= ( )
PR T c d dt t
(3)
(2)(3)
rs
rs
rs( ) ( ) ( ( ) ( )) = (4)
()(N)
rs
rs
rs
rf sc
T f d dt t N( ) ( ) ( ( ) ( ))= + (5)
(datm)
rs
rs
rs
rs
atmfc
T f d dt t N d( ) ( ) ( ( ) ( ))= + + (6)
(differential)
4
GPS
()
GPS
GPS
4.1
GPS
GPS
GPS
(single point positioning)
(relative positioning)
(baseline)[Wells et al, 1986]
7
dr db
B (7)
dr
db dr
B
(7)
GPS
(broadcast ephemeris)(precise ephemeris)
2-3 m GPS
GPS
GPS
GPS1992 1-2m 199410-20cm[Beutler
et al, 1994] 1997 5-10cm [Neilan et al, 1997]
GPS (orbit improvement)[
, 1996]
4.2
GPS
GPS
GPS GPS
(N)
8
N n= ( )1 610 (8)
n
( S )
S =10 (9) 6 Nds
s
GPS
(Ionosphere)(Troposphere)
100 1000
50
(1)
GPS
(TECtotal electron content)
0.51017 electrons/m2 5.01017 electrons/m2
(10) tcf
TEC= 40 32.
c f t
(group delay)
P
10 ns (nano seconds)
100 ns
(magnetic storms) 11
[Dixon,1991].
(3-10) L1 L2
GPS dt
GPS
dt t tL L= 1 2 (11)
(40.3TEC/c) A
A dt f fL L= ( )12
22
2 2 f fL L2 1 (12)
GPS
GPS
GPS L1/L2
(ionospherically free observable)
0.5 ppm [Dodson et al, 1993]
(2)
9
30GHz
GPSL1 L2
GPS
N P T e T e T= +77 642 12 92 3719002
. ( ) . ( ) ( ) (13)
P(mbar)T(K)e(mbar)
N(Nd)(Nw)
10
N P Td 77 642. ( )=
N e T e Tw = +12 92 3719002. ( ) ( )
90%
200-230
( ) csc( ) (e )
GPS [Brunner and Welsch,
1993] GPS
(mapping
function)
(scale factor)
4.3 SA A-S
GPS
[McNeff,
1989] GPS
11
SA (Selective Availability) A-S
(Anti-Spoofing)
(1) SA (Selective Availability)
SA (-process)
(dithering)(-process) [Georgiadou and Doucet, 1990]
SA C/A
20 m 100 m 30 m
156 m
SA
GPS
(2) A-S (Anti-Spoofing)
A-S GPS L1 L2 P
P W Y
Y
A-S GPS P
L2 GPS
A-S L2
(squaring)(cross-correlation)
(code-correlation squaring) P-W (P-W code tracking)
[Ashtech Inc, 1992].
4.4
GPS
12
(mean offset)(variation) GPS
()
(pattern)
8 mm [Braun et al, 1994]
2 10 cm [Larson, 1994]
GPS ()
GPS
GPS GPS
[Schupler and Clark, 1991]
GPS
( Trimble, Rogue Ashtech )
5 GPS
GPS
5.1 GPS
GPS (code
correlation technique) L1
C/A
13
L1
L1 C/A
L1
P P
L1 L2
A-S L2
P L2 A-S
L2 L2
L2 L2
Magnavox Company
Y P P
L2 L2
Allen Osborne Associates Inc
W P L1 L2
L1 L2 L1
Y L2 (Y2-Y1)
C/A C/A + (Y2-Y1) L2
Y1 Y2 L2
Ashtech Inc P-W
P W L1 L2 W
P W
W P GPS
L1 C/A Y1 L2 Y2
L2
5.2
GPS
a, b i (6)a
i b i
14
ai
ai
ai
ai
atmfc
T f d dt t N d( ) ( ) ( ( ) ( ))= + + (14)
bi
bi
bi
bi
atmfc
T f d dt t N d( ) ( ) ( ( ) ( ))= + + (15)
ab b a( ) ( ) ( )= i i i (16)
(14)(15)(16)
abi
ab ab abi
atmif
cT f d N d( ) ( ) ( )= + + (17)
(17)(14)
dt
a, b i, j
abij
abij
abij
atmfc
T N d( ) ( )= + + (18)
d
(1 2)
ijabij
ab atmfc
T d( ) ( )12 12= + (19)
(19)
10 km
L1
10 km L1/L2
L1 L2
5.3
GPS
(the least
squares adjustment)
GPS
GPS (a b)(i j)
15
abij
abij
abijf
cN= + (20)
abij
b a b ai
abij j j if
cN+ +)= ( (21)
a b
ai i
ai
ai
aX X Y Y Z Z= + + ( ) ( ) ( )2 2 2 1 2 (22)
(Xi, Yi, Zi) i (Xa, Ya, Za) a
i j a
b
a b p q
(p - 1) 3 + (q - 1)
V AX L= (23)
A X L
V
(t)(a b)(i
j)
16
a Y a Z a
b Yij
b Zij
b Nij
abij
abij
abij
t
a a a
b b b ab
abij
t X t Y t Z
t X t Y t Z t N
t t V
( ) ( ) ( )
( ) ( ) ( ) ( )
[ ( ) ( ) ]( )
Xij ij ij
Xij
+ + +
+ + +
= +0 (24a)
()
Xij ab
ij ja
ia
Yij
Zij
a
a
t t f X t X X t X( ) ( ) [ ( ( ) ) ( ( ) ) ]= = + 0 0
a aj
ai
abij
a
ja
aj
ia
ai
abij
a
ja
aj
ia
ai
a X c t t
t tY
fc
Y t Yt
Y t Yt
t tZ
fc
Z t Zt
Z t Zt
( ) ( )
( ) ( ) [ ( ( ) )( )
( ( ) )( )
]
( ) ( ) [ ( ( ) )( )
( ( ) )( )
]
= =
+
= =
+
0 0
0
0
0
0
0
0
0
0
(24b)
Xij ab
ij
b
jb
bj
ib
bi
Yij
Zij
b
b
b
t tX
fc
X t Xt
X t Xt
( ) ( ) [ ( ( ) )( )
( ( ) )( )
]= = + 0
0
0
0
abij
b
jb
bj
ib
bi
abij
b
jb
bj
ib
bi
t tY
fc
Y t Yt
Y t Yt
t tZ
fc
Z t Zt
Z t Zt
( ) ( ) [ ( ( ) )( )
( ( ) )( )
]
( ) ( ) [ ( ( ) )( )
( ( ) )( )
]
= =
+
= =
+
0
0
0
0
0
0
0
0
(24c)
Nij ab
ij
abijab
tt
N( )
( )= = 1
A
t t tt t tt t tt t tt t tt t
Xij
Yij
Zij
Xik
Yik
Zik
Xil
Yil
Zil
Xij
Yij
Zij
Xik
Yik
Zik
Xil
Yil
Zil
b b b
b b b
b b b
b b b
b b b
b b b
=
( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )( ) ( )
1 1 1
1 1 1
1 1 1
2 2 2
2 2 2
2 2
1 0 00 1 00 0 1
( )t2
1 0 00 1 00 0 1
(24d)
( a)
(24a)
(i, j, k, l)(t1, t2)
(25a)
17
X
L
t tabij
abij
=
( ) ( )1 10
(25b)
XYZNNN
b
b
b
abij
abik
abil
=
(25c)
t tt tt tt tt t
abik
abik
abil
abil
abij
abij
abik
abik
abil
abil
( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )
1 10
1 10
2 20
2 20
2 20
GPS
6
(topography)(geoid)
(ellipsoid)
6.1 GPS -WGS84
GPS
WGS84World Geodetic System, 1984WGS84
Z BIHBureau International de lHeure
Conventional Terrestrial Pole, CTPX BIH
CTP Y
X [Defense Mapping
18
Agency, 1987]
WGS84
1 GRS80
GRS80 IUGG[Moritz,
1980]WGS84 WGS84
C2,0GRS80 J2
8
1 WGS84
a 63781372 m
GM 39860050.6108 m3 s-2
C2,0 -484.166850.0013010-6
72921150.150010-11
rad s-1
C 2997924581.2 m s-1
f 1 / 298.257223563
6.2 -ITRF
VLBI(Very Long Baseline
Interferometry)SLR(Satellite Laser Ranging) GPS
IERSInternational
Earth Rotation Service ITRFIERS Terrestrial Reference Frame
IERS IAUInternational Astronomical Union IUGG
1987 1988 ITRF
ITRF
ITRF ITRF94 ABC
1993.00 ITRF94
VLBISLRDORIS GPS ITRF94
[Boucher et al, 1996]
SLR GPS
VLBISLR GPS
ITRF92 1988.0
NNR-NUVEL1A
ITRF GPS 1992 IGS(International GPS Service for
Geodynamics)ITRF IGS
GPS IGS ITRF
GPS [Boucher and Altamimi, 1996] GPS
GPS
ITRF
6.3 GPS
(orthometric height)
(mean sea level,MSL)
(geopotential number)
[Heiskanen and Moritz, 1984]
19
W gdHH= = 0 0 C W (26)
C
W
W0
g
dH
(H)
H (27) Cg
=
g (plumb line)
GPS (ellipsoidal height)
GPS
( WGS84)
(normal line)
(h)(H)(geoidal height)
(geoidal undulation) N ( 2)
H h N= (28)
100 m
[Schwarz and Sideris, 1993]
20
P
HTopography
h
NGeoid
Ellipsoid
2
GPSGPS(GPS
heighting) GPS
GPS GPS
GPS
[Zilkoski et al,
1992]
GPS GPS
21
H h N= (29)
H H h h N N2 1 2 1 2 1( ) = ( ) (30)
h GPS N
N
H [Rapp and
Balasubramania, 1992]
GPS
GPS
GPS
7 GPS -IGS
GPS
GPS
Epoch'92 IGS (International GPS
Service for Geodynamics) 1992 GPS
22
[Beutler,
1993] IAG (International Association of Geodesy)
IGS 1994 1 1 GPS
IGS
()(
)(
) (
)[Mueller, 1991]
IGS 150 GPS
IGS GPS (
)IGS GPS
IGS 1-2 m
5-10 cm IGS
ITRF ITRF IERS GPS
ITRF
8
1967 (Geodetic Reference System 1967GRS67)
,
GPS
GPS
WGS84
GPS
GPS
IERS
23
ITRF
[IERS, 1996]
GRS80
GPS ITRF
GPS
GPS 105 617
[,1997]
GPS
GPS GPS
1. GPS
2. GPS
3.
4. GPS
5.
6. GPS
7. GPS
24
GPS
1. 8 GPS 105 617
2. GPS
3. ITRF94 (1994 )
1997TWD97 (Taiwan Datum
1997)
4. GRS80 (1980
)
5. 2 121E
119E
2TM NE
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